A. Sample

Electrochemical experiments were carried out in half cells at 25 °C. The cells were assembled in the standard coin-type CR2032 cases (diameter 20 mm, height 3.2 mm) using a lithium foil (∅ 16 mm, thickness 0.7 mm), a porous polyethylene separator, a graphite electrode (∅ 14 mm), and an electrolyte containing 1.3 M LiPF₆ in EC : EMC : DMC (3 : 4 : 3 w/w). Graphite electrodes were obtained from commercial prismatic cells and consisted of 98% graphite, 0.8% carboxymethyl cellulose (CMC) and 1.2% styrene-butadiene rubber (SBR); electrode thickness was 74 µm (including Cu foil thickness 8 µm), density – 1.62 g cm⁻¹. Coin cells were assembled in an Ar-filled glove box.

All cycling tests were performed galvanostatically between 1.5 and 0.01 V (vs. Li/Li⁺) at a rate of C/20 (~0.3 mA) using a Bio-Logic VMP3 potentiostat (Bio-Logic, France). Before XRD investigations, the cells were charged to certain SoC (0, 20, 40, and 50%), held 6 h at open-circuit potential and then dismantled in the glove box. Since dQ/dV peaks for LiC₃₀ → LiC₁₈ and LiC₁₈ → LiC₁₂ processes are overlapped (Figure 1), it is impossible to obtain pure LiC₁₈. For simplicity, the charging was stopped at SoC 40% in order to make sure that only LiC₁₈ and LiC₁₂ exist in the anode. Fully charged LiC₆ is not interesting for the present study and its refinement can be found elsewhere (Guerard and Herold, Reference Guerard and Herold1975).

Figure 1. (a) Typical charge/discharge curve of the Li/graphite coin cell (3rd cycle at the rate of C/20) in the voltage range 0.3–0.01  and (b) corresponding differential capacity (dQ/dV) plot. The voltages corresponding to the analyzed samples are marked by the asterisks.

Anode circles taken out from the coin cells were washed with dimethyl carbonate (DMC) to remove electrolyte and covered by kapton film in glove box. Then the XRD patterns were taken in air. Preliminary analysis revealed that during data collection time anodes degrade <2%.

B. Data collection

X-ray powder diffraction data were collected with Philips X-PERT PRO diffractometer (CuKα radiation, PIXCel SSD, diffracted beam graphite monochromator, 40 kV, and 40 mA) using continuous scan mode (2θ range of 20°–105°, step size 0.013°, scan rate 0.67° min⁻¹, and 300 s step⁻¹). The incident slit size (1/2°) was selected taking into account the goniometer radius (240 mm) in such a way to make sure that the size of the irradiated spot remains smaller than the size of the analyzed electrode in the whole measurement range.

C. Data reduction

The obtained diffraction data were converted to the GSAS file format without any additional treatment. Strictly speaking, the high transparency of the graphite layer should lead to the violation of the constant volume assumption and lead to the incorrect determination of the relative peak intensities. However, the contribution of this error is relatively small if there are no low-angle peaks at the diffraction pattern and we did not observe any difference in the refinement results after application of the known corrections to the raw data.

Rietveld refinement was performed using GSAS package (Larson and Von Dreele, Reference Larson and Von Dreele2004) with EXPGUI interface (Toby, Reference Toby2001). Peak shape and reflection asymmetry owing to axial divergence were described by Pseudo–Voigt function (CW function 3 in GSAS). The March–Dollase function with (001) direction of the preferred orientation was chosen to describe the texture of the anode phases. Occupancies of the Li atoms for LiC₁₈ and LiC₃₀ phases were fixed, since their refinement resulted in meaningless deviations from the expected values. z coordinates of the C3 and C4 atoms in the LiC₁₈ and LiC₃₀ phases (Table I) were constrained to be equal in order to keep the corresponding carbon layers flat. Additionally, the fractional coordinate z of the Li atom in the LiC₁₈ phase was constrained in such way to position it exactly in the middle of the interlayer space.

Table I. Crystallographic data for Li _x C₆ compounds.

^a 2/9 for LiC₂₇ composition.

^b (Ohzuku et al., Reference Ohzuku, Iwakoshi and Sawai1993).

Peaks of highly textured copper current collector were fitted using March–Dollase function with three directions of the preferred orientation: (001), (011), (111). Strictly speaking, this should be regarded not as a real orientation in three separate directions but as a series expansion of the real texture. Only the sample shift parameter has physical meaning for the anode phases because of finite thickness of the anode material. This parameter was constrained to be equal for all Li _x C₆ phases. Zero shift for copper phase was refined using both sample shift and transparency corrections.

Peak broadening anisotropy was described by microstrain broadening terms Lij. This description results in a loss of physical information related to stacking faults but it allows one to easily achieve reasonable fitting and to obtain correct structural data and phase composition. Only the Lij terms significantly deviating from zero (usually, L13 and L23) were refined and others were fixed as 0.

Theoretical XRD patterns were calculated in the PowderCell program (Kraus and Nolze, Reference Kraus and Nolze1996). March–Dollase preferred orientation parameter of 0.7 (that is close to experimental parameters for investigated anodes) was applied.

A. XRD for Li–C system

The main structural transformations during intercalation of the Li atoms into graphite and a change of corresponding theoretical XRD patterns are shown in Figures 2 and 3, respectively. This sequence is well known (Ohzuku et al., Reference Ohzuku, Iwakoshi and Sawai1993; Billaud et al., Reference Billaud, Henry, Lelaurain and Willmann1996). Position of the first interplanar peak (Figure 3(a)) sequentially decreases with an increase of the Li content and corresponds to average interplanar C–C separation. Three phases in the Li _x C₆ system, namely LiC₆, LiC₃₀, and graphite are well distinguished by their peak positions and intensities. In contrast, the XRD patterns for LiC₁₈ and LiC₁₂ compounds are very similar because of their close lattice parameters ( $a_{{\rm LiC}_{18}} \approx a_{{\rm LiC}_{12}} /\sqrt 3 ;\;c_{{\rm LiC}_{18}} \approx c_{{\rm LiC}_{12}} \times 2$ ) and can be easily mixed up in experimental patterns (Figure 4).

Figure 2. (Color online) Structural transformations in lithiated graphite with ordered Li-layers sequence.

Figure 3. Theoretical XRD patterns for compounds in the Li _x C₆ system. Dash lines indicate position of Cu-peaks from current collector.

Figure 4. Experimental XRD patterns for anodes with different SoC. Reflections from the Al₂O₃ phase are marked with asterisks.

An interpretation of the experimental XRD patterns in some cases may be rather difficult since the real FWHM (full-width at half-maximum) values are usually noticeably bigger than those shown in Figure 3. A strong preferred orientation considerably decreases the number of peaks suitable for phase and structure analysis. Furthermore, a presence of stacking faults contributes in additional changes resulting in distortion of peak shape. Most of the peaks of LiC₁₈ & LiC₁₂ are strongly overlapped, therefore, careful profile analysis should be used for phase identification and low-intensity peaks become extremely important. Unfortunately, the $\left\{ {101} \right\}_{{\rm LiC}_{18}} $ peak is overlapped with the {111} peak of copper current collector and cannot be used for phase identification. Additionally, the $\left\{ {103} \right\}_{{\rm LiC}_{18}} $ peak is usually strongly broadened because of stacking faults and it becomes almost invisible in the diffraction patterns.

The most prominent difference between these two phases is the strong difference between intensities of the $\left\{ {110} \right\}_{{\rm LiC}_{18}} $ and $\left\{ {100} \right\}_{{\rm LiC}_{12}} $ peaks at ~42.1° and between intensities of the $\left\{ {112} \right\}_{{\rm LiC}_{{\rm 18}}} $ and $\left\{ {104} \right\}_{{\rm LiC}_{12}} $ peaks at ~49.8°. The easiest practical way to distinguish between LiC₁₈ & LiC₁₂ phases is a structural refinement using full profiles since it takes into account not only peak positions but intensities as well. A correct choice of profile function allows us to perform suitable fitting even when a part of diffraction lines are strongly broadened owing to the presence of stacking faults. Therefore, a contribution of every particular phase in the overall diffraction peak intensity may be determined. Additional and very important practical advantage of structural refinement is the possibility to quantify a weight fraction for every Li _x C₆ phase in the mixture and consequently, estimate a real SoC of anode.

B. Structural characterization

Table I contains crystallographic data for compounds in the Li _x C₆ system. It is worth noting that the structural information for some of Li _x C₆ compounds found in the literature is difficult to use. For example, only layers sequence is given for LiC₃₀ (Billaud and Henry, Reference Billaud and Henry2002) and a structure of LiC₁₈ is reported to depend on the way of its preparation (Billaud et al., Reference Billaud, Henry, Lelaurain and Willmann1996). Therefore, we decided to collect the data together for easier usage in the future. Figure 5 shows the result of Rietveld refinement for anodes listed in Table II. One can see from the difference curves the refinement is suitable despite that the XRD data are not of high quality. A use of variable divergent slit for data collection looks more preferable because the X-ray spot fits the electrode area over the whole angle range.

Figure 5. (Color online) Results of Rietveld refinement for anodes with different SoC. Numbers refer to following phases: 1, graphite (black); 2, LiC₃₀ (green); 3, LiC₁₈ (violet); 4, LiC₁₂ (orange); 5, Cu (blue); 6, Al₂O₃ (red).

Figure 6. (Color online) Results of Rietveld refinement for anode with 40% SoC: (a) LiC₁₂ and LiC₁₈ included in the refinement; (b) only LiC₁₂ included; (c) only LiC₁₈ included. Positions of the most important reflections for analysis are marked by arrows in the difference curves. Colors and phase numbering correspond to Figure 5.

Table II. Electrochemical characteristics and phase composition for anodes.

^a Corresponding refining results are shown in Figure 6.

Structural refinement confirmed our above suggestions made by careful phase analysis: it is possible to prove existence of both LiC₁₈ and LiC₁₂ phases and refine their content. The SoC values were calculated from phase fractions and the SoC values corresponding to each phase. They well correspond to those expected from the charging conditions (Table II).

The main expected differences between the XRD patterns of LiC₁₂ and LiC₁₈ are intensities of the subcell $\left\{ {110} \right\}_{{\rm LiC}_{12}} /\left\{ {100} \right\}_{{\rm LiC}_{{\rm 18}}} $ and $\left\{ {112} \right\}_{{\rm LiC}_{{\rm 12}}} /\left\{ {104} \right\}_{{\rm LiC}_{18}} $ reflexes and the absence of superstructural $\left\{ {103} \right\}_{{\rm LiC}_{18}} $ peak in the pattern of LiC₁₂ (Figure 5). The superstructural $\left\{ {103} \right\}_{{\rm LiC}_{{\rm 18}}} $ peak is strongly broadened owing to the presence of stacking faults and becomes almost invisible in the XRD pattern. The $\left\{ {101} \right\}_{{\rm LiC}_{18}} $ peak is overlapped with the {111} peak of copper and cannot be used for phase identification. Generally, the refinement was carried out mainly with peaks of [00l] and [hk0] zones. A change of the intensities of the $\left\{ {110} \right\}_{{\rm LiC}_{12}} /\left\{ {100} \right\}_{{\rm LiC}_{18}} \;{\rm and}\;\left\{ {112} \right\}_{{\rm LiC}_{{\rm 12}}} /\left\{ {104} \right\}_{{\rm LiC}_{18}} \,$ peaks is well visible in Figure 5 for 50 and 40% SoC, respectively. At the same time intensity of the peak at 52° 2θ remains nearly the same with noticeable broadening at 40% SoC in comparison with 50% SoC where only LiC₁₂ phase is present. The broadening is because of overlapping of the $\left\{ {004} \right\}_{{\rm LiC}_{12}} \;{\rm and}\;\left\{ {008} \right\}_{{\rm LiC}_{18}} $ peaks.

The values of weight concentrations for every phase give real SoC (Table II). In the proposed case, these values are close to expected ones whereas a refinement 40% SoC pattern as single LiC₁₈ leads to a value of SoC 33%.

The size/strain characteristics cannot be extracted or even correctly estimated from the existing data and it was not a goal of the present work. However, it is important to say a few words about texture parameters for Li _x C₆ phases. Texture parameters are different for lithiated phases. For example, in case of the sample used in the current work for refinement of the LiC₁₈ structure the March–Dollase coefficients are 0.602 for the LiC₁₂ phase and 0.740 for the LiC₁₈ phase. This difference means that the naïve determination of the LiC₁₈/LiC₁₂ ratio using only the intensities of the strongest peaks would lead to ~2 times smaller value than the real one and corresponding overestimation of SoC. Moreover, the texture parameters vary with a change of state of charge (a detailed study will be published separately). From this point of view a quantification based on intensity ratios for {002} or {004} peaks may result in a noticeable deviation from the real concentration values.